Binary multiplying circuit



May 12, 1953 BINARY MULTIPLYING` Original Filed June 24, 1943 G. C. HARTLEY ET AL CIRCUIT 4 Sheets-Sheet l 'iA-YJ W 4 @as l y M @f-92 Q aL-e v .'{Ww} fyi 41% #7.1M il@ @T91 ZX May 12, 1953 G. c. HARTLEY ETAL u 2,638,267

BINARY MULTIPLYING CIRCUIT Original' Filed June 24, 1945 4 Sheets-Shet 2 May 12, 1953 G. CQHARTLEY ET AL 638,267

' BINARY MULTIPLYING CIRCUIT original Filed Jupe 24, 1943 i 4 sheets-sheet s 27 y i. H63.

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May l2,- 1953 G. c. HARTLEY ET AL- 2,638,267

BINARY MULTIPLYING CIRCUIT Orignall Filed June 24, 1943 4 Sheets-Sheet 4 Patented May 12, l1953 BINARY MULTIPLYING CIRCUIT George Clifford Hartley and William John Reynolds, London, England, assignors, by mesne assignments, to International Standard Electric Corporation, New York, N. Y., a corporation of DelawareI v 'Continuation of application serial No. 492,060, June 24, 1943. This application February 28,

194s, serial No. 11,8 1o, 1941 Y 96. In Great Britain May section 1, Public Law 69o, August e, 1946 Patent expires May 10, 1961 This invention relates to electrically operated calculating equipment for performing multiplication operations, and is a continuation of application Serial No. 492,060, led June 24, 1943, now abandoned.

In application Ser. No. 494,282, filed July 12, 1943, now Patent No. 2,601,281, there has been described and claimed electrically operated calculating equipment arranged to perform calculations -in radix 2. The particular calculations described were those of addition and subtraction. A

According to one feature of thepresent invention electrically operated calculating equipment is arranged to perform multiplication operations in radix 2.

A number in radix two will have 2 as a base instead of 10, which is the base of the ordinary numbering system. Each digit of a number in ,radix two is either or 1. When 1 is added to a ,digit of a radix two number and the resultant comes to more than 1, 0 is entered and 1 carried to the next-denomination. The radix two numbers lcorresponding to radix 10 numbers from 1 to 12 are as follows: i

Radix an Radix two Radix ten Radix dvd 'I'he nature of the invention will be better understood from the following description taken in conjunction with the accompanying drawings in which:

Fig. 1 is a circuit diagram of a portion of one form of the apparatus.

Figs. 2 and 3 are circuit diagrams of the remaining portions of the apparatus; and

Fig. 4 is a circuit diagram of a portion of the circuit of Fig. 1 showing a modified form for obtaining an approximation. l

The drawings show electric circuits by means of which a multiplicand m'ay be entered into electrically operated calculating equipment, the calculation performed in radix two, and the resultv of the multiplication automatically obtained. In the circuits shown the multiplicand and the multiplier are entered as numbers expressed in radix two and the solution obtained as a number expressed in radix two. Provision is. made for entering numbers of up to six denominations.

5 Claims. (Cl.l 235-61) In the drawings relays have been designated by a letter or letters. The contacts for these relays are shown distributed over the various figures in the circuits which they control, rather than in close association with the relays to which they belong. The contacts are designated by the letter or letters of the relay tov which they belong followed by a number to differentiate contacts of the same relay. This arrangement'avoids a complex wiring diagram and makes the drawing easier to read and understand. Filled-in arrows have been used to represent battery throughout the several figures.

The circuits are such as to carry out operations exactly analogous to those performed in long hand multiplication. Consider the manner in which a number, the successive digits of which are a, b, c, d, e, f (in radix two) is multiplied by another number, the successive digits of which are a', b', c', d', e', j'.

The calculation can be set down s follows:

C ci

tl b

l1 c b a b c The rst row represents the multiplicand, the second row the multiplier. Succeeding rows represent the partial products obtained by multiplying the digits of the multiplicand by successive digits of the multiplier starting from the digit of lowest denomination. As each digit of the multiplier can only be 1 or 0,'each row represents the multiplicand displaced one denominational `pl-ace as compared with the row above and it must be considered that a row is omitted if the corresponding digit of the multiplier be 0.- The solution is then obtained by adding the digital values in each denomination and carrying over any necessary values to be included in the total to 1be obtained for the next higher denominational va ue.

Referring to the drawings, Fig. l is a circuit diagram of an apparatus for obtaining the partial products to be added in order to obtain the solution. The multiplicand is entered on the terminals I, there being one terminal for each digit of the multipli-cand. The value of each digit is represented by the presence or absence of ground on the corresponding terminal in entering the digit, ground being applied if the digital value be one, and there is no ground if the digital value be (l. The multiplier is entered in a similar manner on terminals M. Relays YLT-YZ are operated or not operated in accordance with the value of the respective digits of the multiplier. The remainder of the relays shown in Fig. 1 then become operated or remain unoperated in accordance with digital values of the products of the digits oi the multiplica-nd and the multiplier.

The separate terminals of the setsV of termi'- nals I and M are denoted by the denominations of the corresponding digits.. If the digits of lowest denomination in the multiplier has 'the value 1, relay YZ is operated and by its contacts YZl-YZB connects the terminals I for the the respective denominations 2 25 to .relays ZZ-ZU. Those of the last mentioned relays which corresponding to digits of the multiplicand having the value 1 accordingly operate, Athose corresponding to digits of the multiplicand havi ing the value remain unoperated. If, on the other hand, the digit of lowest. denomination Vin the multiplier has the value 0, relay`YZ is not operated and none vof the relays ZZ-AZU is operated. Thus the operated or nom-operated conditions of the relays ZZ- ZU represent the products of the respective digits of the multiplicand by the digit of lowest denomination, i. e; 2 in the multiplier.

Similarly, the operated or non-*operated conditions of the relays XT-XY represent the values of the' products of the respective digits of the multiplicand by the digit or denomination 21 in the multiplier. As any one of these products involving a particular digit of the multiplicand is of the next higher denomination to the corresponding product involving the digit of denomination of the multiplicand, the relays XY-XT have been shown displaced ascompared with the corresponding relays ZZ-Zll Similarly, the `other partial products are represented by the other relays. If the above mentioned calculation be now set down again with the relay designations for the digits the values of which the conditions of the relays represent, it will appear as follows:

a b c d e f YU Yv YW YX YY YZ The result of the calculation may then ybe obtained by adding together the values of the digits represented by the conditions of the relays in the columns shown above, starting from the right, carrying over any necessary values t0 be included in the addition for theA next higher denomination.

The circuits for performing this addition are shown in Figs. 2 and 3 which contain the contacts of the relays of Fig. 1 with certain additional relays and contacts. divided into sections, each showing the circuit for the addition for a given denomination. The solution is obtained on lamps LA--LL which are shown scattered around on the figures, lamps LA-LF being shown in Fig. 3, while lamps LG-LL are shown in Fig. 2. There is one lamp for each digit, the circuit for a lamp being completed if the value of the digit is 1, so that in such case the lamp is lit. A lamp is not lit .if the value of the corresponding digit is zero.

Figs. 2 and 3 are '4 .'.tlne solution `,is obtained substantially instantaneously', i. e. in one stage only and the time taken being only that required to operate a few fast operating relays in immediate succession.

In obtaining the sum, the following principles are utilised:

'(.al- In lany column, representing a particular denomination, the answer in that column is 1 if the total of the column and carry over is odd, and the Aanswer is (l if such total is even.

(b) The carry over to the column of next higher denomination is the number of pairs in the suml of the column total and the carry over.

The `digit of lowest denomination is represented by lamp LL (Fig. 2, center right), the circuit `vof which .is completed at front contacts ZZ{,'if ZZ, (Fig. 1), is operated. It is clear that relay ZZ could be omitted and the circuit of lamp LL completed directly from terminal 2 of the set I over front contacts YZI.

LampLK represents the digit of denomination 21, its circuit being completed Aover contacts ZY! back and- XY! front, or ZY! iront and XYi back. If both relays ZY and XY are operated, there is no circuit for lamp LK, and a carry over relay XJA is operated by front contacts XYZ t0 carry over a digital value to denomination 22.

Lamp LJ vrepresents the digit of denomina tion 22. Its circuit is completed if an odd number of the four relays ZX, XX, WX and. XJA is operated, and is not completed if an even number-oi these relays is operated.

The contacts over which the circuit of the lamp is completed are:

The value to be carried over to the' next higher denomination is2, if all four relays are operated, or 1, if any two or three out of the four relays are operated, or 0,- of one only or none of .the four-'relays is operated. Relays XIA and XIB are providedv for this purpose. Relay XIA is operated over' ZX? front, XX@ front, if both relays ZX and XX are operated, or over ZX? iront, XXll back, WX4 iront if both relays ZX and WX are operated, and relay XX is not operated, whilst relay XIB is operated if all four relays are operated over ZX! front, XXZ front, lli/'X3 iront', XJAS front, or, if relay ZX is operated, both relays XX and WX are not operated (so that relay XIA is not operated), and relay XJA is operated over ZX2 iront, XX@ back., WXli back, XJAS front'. Thus, one or the other of the carryover relays XIA and XIB is operated whenever there is l to carry over to denomination 23, and whenever therev is 2 to carry over, both relays XIA and XIB are operated.

For denomination 23, the circuit of the lamp LI depends on the four relays ZW, XW, l'lrv' and VW, representing digits of the partial products and the two relays XIA, XIB representing carry over amounts from denomination 22. The circuits for the lamp LI and for relays Eil-IA, XHB, XH@ ior'carry over to the next higher denomination wiil be clear from comparison with those explained above, bearing in mind the two principles set out previously. When there is 1 to front, XXZ back, WX2 back, XJAZ back. front, XX2` back, WX? front, XJA! iront. front, XXZ `front', WX! back, XJA! iront. front, XX2 front, WX! front, XJAZ back. back', XX! back, WX! back, XJA! front. back, XX! back, WX! front, XJAZ back. back, XX! front, WXZI back, XJAZ back. back, XX! front, WX2 front, XJA! front.

carry over to denomination'24, one of the carry:

l24, two of thesey relays will operate; and when there is 3 to carry over .to denomination 24, all three of these relays will operate.` l

The circuits of lamps LH, LG,'LF, LE, LD, LC and LB will also be clear from the above explanation of the circuits for the lampLJ. XGA, XGB, XGC, XGD are relays for the'carryover from denomination 24 to denomination 25, XFA,4 XFB, XFC, XFD, XFE relays for carry over from denomination 25 to denomination 26 (shown in Fig. 3), XEA', XEB, XLEC, XED, XEE for carry over from denomination 2s to; 2", XDA, XDB; XDC, XDD from 2'?, to 28, XCA, XClEi, XCC from 28 to 29, and XBA and XBB from 29 to 21. Relay A determines by its condition whether carry over is to take place into the highest denomination 211. Contacts AI thus determine whether lamp LA is to be operated for the digit of highest denomination in the solution.

It is clear that the circuits shown can be readily extended for the multiplication ofy numbers having any number 1 of digits. In the case of numbers having a large number of digits, an approximate solution can be obtained by omitting the last three lamps in the circuits shown, so that the last three digits are always zero. Approximation to a certain number of signicant iigures may be obtained by omitting the relays of Fig. 1 for the unwanted digits and their associated relay chains and lamps of Figs. 2 and 3. For an approximation to N significant figures the relays for adding the partial products for the (N-l-n) highest denominations in the solutions are retained, the others being omitted and N digits only exhibited in the solution. Generally n would not be less than 3 but is value depends on the accuracy required. For this purpose certain of the relays in Fig. 1 may be connected into the circuits shown in that gure over the normally closed contacts of keys, which, when operated, accordingly remove those relays from the circuit. Suppose, for example, as indicated in` Fig. 4, that relays ZX, XX, WX, ZY, XY and ZZ are connected through the normally closed keys KI and the keys are thrown to remove them from circuit. Relays ZX, XX and WX will each represent 1 inthe 22 denomination; relays ZY and XY will each represent 1 in the 21 denomination; 1

and relay ZZ will represent 1 in the 2 denomination. The maximum number that can be thus lost is l-i-lO-l-lO-l-lOO-i-lOO-f-IOO (i. e. 10001) and the error thus introduced may be averaged by adding approximately one half of this nurnber or a digital value 1 in denominationA 23.' This may be done by providing an additional winding K2 on relay XIB of the 22 denomination over which the relay is operated from a contact K3 of the key or keys which removed the relays ZX-ZZ from the circuits.

It is clear that, if it be desired to transfer the result of the multiplication to some other circuit, for further operations to be performed on such result, or for other purposes, the lamps LA, LL may be replaced by relays.

What is claimed is:

1. An electrically operated calculating apparatus for performing multiplication of numbers in binary form comprising a plurality of relays arranged electrically in rows with the last relay of rowfor each digit of a multiplicand to b e entered into said apparatus,an individual operating circuit for each relay including a switch to connect said relay to said operating circuit, a separate means for each row of relays simultaneously to control said switches associated with all, the relays of that row, said operating ycircuits of each row being connected respectively to the circuits of all the other rows in the same sequenceV along the rows, means to` energize-said operating circuits for a combination of said relays determined by the digital values of a multiplicand entered intosaidapparatus, means to close the switches in' a combination of rowsmofH said relays determined by -the digital values of a. multiplier entered-into said apparatus, a plurality of registering devices, there being one for each column of said relays, carry-over control devices for each column, separate energizing rcircuits associated respectively with said devices, the energizing vcircuits for a particular devicev containing contacts of the relays in the column ofrelays associated with that device, and means in each of said circuits controlled by the relays in the corresponding column, further means in each of said kcircuits controlled by the carry-over control devices of the next lower column, each ofsaid'circuits controlling the energization' of its registering device so as to register a digital value for the corresponding denomination of the product of said multiplicand and said multiplier and to determine carry-over to the next higher denomination thereof.

2. An electrically operated calculating apparatus as dened in claim '1, in which the carryover control devices of each column comprise additional relays, and in which said additional relays of each column control contacts in the energizing circuit of the next higher column.

3. An electrically operated calculating apparatus for performing multiplication of numbers in binary form comprising a plurality of relays arranged electrically in rows with the last relay of each row lined up with the next to the last relay of the next adjacent row to form columns of relays corresponding to the columns used in longhand multiplication, there being a relay in each row for each digit of a multiplicand to be entered into said apparatus, an individual operating circuit for each relay including a switch to connect said relay to said operating circuit, a separate means for each row simultaneously to control said switches associated with all the relays of that row, said operating circuits of each row being connected respectively to the circuits of all the other rows in the same sequence along the rows, means to energize said operating circuits for a combination of said relays determined by the digital values of a multiplicand entered in to said apparatus. means to close the switches in a combination of rows of said relays determined by the digital values of a multiplier entered into said apparatus, a plurality of registering devices, there being one for each column of said relays, carry over control devices for each column, separate energizing circuits associated respectively with said devices, means in each of said circuits controlled by the number of relays in the corresponding column, further means in each of said circuits controlled by the carry over control devices of the next lower column, each of said circuits controlling the energization of its registering device so as to register a digital value for the corresponding denomination of the prodhand multiplication, there beinga relayrhieach to determine carry-over to.` theV next higher denomination thereof, andv means to disconnect certain of said relays corresponding tok a predeterminednujnber of dig-its at the e'ndofsaid product and the corresponding' registering de-vices to carry over a value of l to the denomination next above the highest denomination of the discenn'ected relays, whereby an approximation f the product is obtained as a 'predetermined nuiillte'rJ of significa-nt` digits.

4. Electrically' operated apparatus for multiplying' 'a multi-digit multiplicand, expressed in' radix two; by al multi-digit multiplier, also cx# pressed in radix two, comprising va siiil series' of relays representing the respectiyeV digits of the multiplier, a plurality of series of' relays rep'- resent'ng the respective digits of each successive partial 'product obtained by the successive multiplication f 'the complete multpli'cand by therespective digitsl of 'thel multiplier', the mimber of suoli partial piduts and llietefoi'ef the riurlbi of Series 0f Such partial product 'riel'ays-l being; thusl equal to the number' of digits of the. multi` plier, means' including contacts operated by said single`I series of multiplier relays forv controlling energ'i'zation ofA saidplurality of seriesv of partial productrelaysf, a pluralityy of index elements,

means? including: a plurality oi parallel circuits,

each'said circuit including' one of said index eleuneiitsandv each 'also including contacts for ccntrolling energizatio-n of said index elements, which contacts are operated by distinct groups of partial product relays, and' which distinct groups include relays representative of successive partial produots said index elements adapted to indicate sum of all said partial products.

5. Apparatus, as denedi in claim 4, wherein said" last-named means includes the contacts of a; plurality of' carry-over relays and circuits for energizing said` relays, the energizing circuit for each of-s'aid carry-over'relays including at leas-t i one.y contact of 'a partial prod-uct relay representing a preceding order from that of the index element centrolled byV said relay.

1 v GEORGE CLIFFORD HARILEY.

WILLIAM JOHN REYNOLDS,

References Cited in the le of this patent UNITED STATES' PATENTS Number Name Date 2,192,612' Larigt al Mar. 5, 1940 v2,318,591 C'oufgnal May 11, 1943 FOREIGN PATENTS Number Country Date 410,12'9 Gieat IB'i'it'aill Mayv 9, 1934 

